Area Calculator: Calculate the Area of 17 Common Shapes

Use our Area Calculator to calculate the area of squares, circles, triangles, rectangles, polygons, and more. Find area, use different units, and solve missing dimensions.

The Area Calculator helps you quickly calculate the area of different geometric shapes. Choose a shape, enter the required measurements, and the calculator automatically applies the correct area formula to give you the result.

It supports 17 common shapes, including squares, rectangles, triangles, circles, semicircles, sectors, ellipses, trapezoids, parallelograms, rhombuses, kites, regular polygons, and annuli. You can also use different length and area units, and work backward from a known target area to find a missing dimension.

Whether you’re working on a geometry problem, estimating the floor area of a room, planning a garden, or measuring a circular or ring-shaped space, this tool can save you from remembering a long list of formulas and doing repetitive calculations by hand.

What Is Area?

Simply put, area tells you how much two-dimensional space a shape covers.

Imagine you’re getting ready to paint a wall. What you really need to know isn’t just how long the wall is, but how much surface needs to be covered. The same idea applies when you’re laying flooring, planning a lawn, measuring land, or designing a garden bed.

Area comes up in everyday situations all the time:

• How much flooring does a room need?
• How much wall surface needs to be painted?
• How large is a garden or lawn?
• How much land does a property cover?
• How much surface does a tabletop have?
• How large is a classroom or office floor?
• How much space does a circular area cover?
• How large is a ring-shaped garden bed or pathway?

Because area describes two-dimensional space, it is normally expressed using square units, such as square centimeters (cm²), square meters (m²), or square feet (ft²).

Area, Perimeter, and Volume: What’s the Difference?

These three measurements are easy to mix up, but they describe different things:

• Length measures the distance from one point to another.
• Perimeter measures the distance around the outside of a shape.
• Area measures the surface covered inside a two-dimensional shape.
• Volume measures the three-dimensional space occupied by an object.

A simple way to remember them is:

Length measures a line, perimeter measures a boundary, area measures a surface, and volume measures three-dimensional space.

For example, consider a room that is 6 meters long and 4 meters wide:

• Perimeter = 2 × (6 + 4) = 20 m
• Floor area = 6 × 4 = 24 m²
• If the ceiling is 2.8 m high, volume = 24 × 2.8 = 67.2 m³

So if you want to know how much flooring you need, you need the area. If you want to estimate how much baseboard is needed around the room, you need the perimeter.

What Is an Area Calculator?

An Area Calculator is an online tool that helps you calculate the area of geometric shapes.

You choose the shape, enter the required measurements, and the calculator uses the appropriate area formula to calculate the result.

It can be useful for:

• Learning and reviewing geometry formulas
• Checking math homework
• Estimating floor areas
• Estimating wall and surface areas
• Planning gardens and flower beds
• Comparing the size of different areas
• Design and space planning
• Working with circles, sectors, annuli, and other less familiar shapes

The goal is simple: instead of remembering a different formula for every shape, you can enter your measurements and let the calculator handle the mathematics.

Why Was This Area Calculator Developed?

In real life, area calculations are not always as simple as length × width.

A room may be rectangular, but a tabletop could be circular, a garden bed could be ring-shaped, and part of a building or design could have a triangular, trapezoidal, or sector shape.

Different shapes require different formulas, and that’s where things can get complicated.

You may need to remember:

• When to divide by 2
• When to use π
• Which measurement is the perpendicular height
• How to use diagonals
• How an angle affects a sector
• How the number of sides affects a regular polygon
• How to convert centimeters into meters or other units
• How to work backward when the area is known but one dimension is missing

The purpose of this calculator is to bring these common calculations together in one place.

You provide the shape and measurements, and the calculator handles the formula, unit conversion, and calculation.

How to Use the Area Calculator

Using an Area Calculator usually takes just a few steps.

1. Choose a Shape

Start by selecting the geometric shape that best matches the area you want to measure.

For example:

• Room floor → Rectangle
• Square tile → Square
• Round tabletop → Circle
• Pizza-shaped region → Sector
• Ring-shaped garden bed → Annulus
• Regular geometric design → Regular Polygon

2. Enter the Required Dimensions

Each shape requires different measurements.

For example:

• Square → side length
• Rectangle → length and width
• Triangle → base and height
• Circle → radius
• Sector → radius and angle
• Rhombus → two diagonals
• Ellipse → semi-major axis and semi-minor axis

3. Choose Your Units

Use the units that match your measurements.

For example, if you measured a room in centimeters, you can enter the measurements in centimeters.

If you want the final answer in square meters, you can select square meters as the output unit.

4. Check the Result

The calculator applies the appropriate formula and displays the calculated area.

5. Review the Formula and Calculation

You can also review the formula and calculation steps to see how the result was obtained.

This can be particularly useful when learning geometry, checking homework, or verifying a manual calculation.

How Is Area Calculated?

There is no single area formula that works for every shape.

Different shapes have different geometric properties, so each one requires its own calculation method.

For example:

• A rectangle uses length × width.
• A triangle uses its base and perpendicular height.
• A circle uses its radius and π.
• A sector also requires a central angle.
• A rhombus or kite can use its two diagonals.
• A regular polygon depends on its number of sides and side length.

Once you choose the correct shape, the corresponding formula can be applied.

Below are the 17 shapes supported by this Area Calculator and the formulas used to calculate their areas.

Area Formulas by Shape

Square

Formula:

Area = side²

A square has four equal sides, so you only need the length of one side.

For example, a square with a side length of 5 m has:

5 × 5 = 25 m²

Its area is therefore 25 m².

Rectangle

Formula:

Area = length × width

The area of a rectangle is found by multiplying its length by its width. This is one of the most commonly used area formulas in everyday life.

For example, a room that is 6 m long and 4 m wide has:

6 × 4 = 24 m²

So the floor area is 24 m².

Triangle

Formula:

Area = 1/2 × base × height

To calculate the area of a triangle, multiply the base by the height and divide by 2.

There is one important detail: the height must be the perpendicular distance from the base to the opposite vertex. It is not simply the length of any sloping side.

For example, if the base is 10 m and the height is 4 m:

1/2 × 10 × 4 = 20 m²

The area is 20 m².

Circle

Formula:

Area = π × radius²

The area of a circle is calculated using its radius.

π (pi) is approximately 3.14159, and the radius is the distance from the center of the circle to its edge.

For example, if the radius is 3 m:

π × 3² ≈ 28.27 m²

So the area is approximately 28.27 m².

If you know the diameter instead of the radius, divide the diameter by 2 to get the radius.

Semicircle

Formula:

Area = 1/2 × π × radius²

A semicircle is exactly half of a full circle, so its area is also half the area of the corresponding circle.

For example, with a radius of 2 m:

1/2 × π × 2² ≈ 6.28 m²

Sector

Formula:

Area = (angle / 360) × π × radius²

A sector is a portion of a circle.

A complete circle has an angle of 360°, so the central angle tells you what fraction of the circle the sector represents.

For example:

90 ÷ 360 = 1/4

A 90° sector therefore represents one quarter of the full circle.

If the radius is 2 m:

1/4 × π × 2² ≈ 3.14 m²

Ellipse

Formula:

Area = π × semi-major axis × semi-minor axis

Unlike a circle, an ellipse does not have a single radius. Instead, it has two semi-axes:

• Semi-major axis — half of the longest axis
• Semi-minor axis — half of the shortest axis

For example, if the semi-major axis is 3 m and the semi-minor axis is 2 m:

π × 3 × 2 ≈ 18.85 m²

The area is approximately 18.85 m².

Trapezoid

Formula:

Area = 1/2 × (base 1 + base 2) × height

A trapezoid has two parallel sides, which are the two bases.

The height is the perpendicular distance between those parallel sides.

For example, if the two bases are 5 m and 7 m and the height is 4 m:

1/2 × (5 + 7) × 4 = 24 m²

Parallelogram

Formula:

Area = base × height

The area of a parallelogram is the base multiplied by its perpendicular height.

The height is the perpendicular distance between the two parallel bases. It is not necessarily the length of the sloping side.

For example, with a base of 6 m and a height of 3 m:

6 × 3 = 18 m²

Rhombus

Formula:

Area = 1/2 × diagonal 1 × diagonal 2

The area of a rhombus can be calculated using the lengths of its two diagonals.

For example, if the diagonals are 8 m and 6 m:

1/2 × 8 × 6 = 24 m²

Kite

Formula:

Area = 1/2 × diagonal 1 × diagonal 2

A kite is a quadrilateral with two pairs of equal adjacent sides. Its area can also be calculated using its two diagonals.

For example, if the diagonals are 10 m and 7 m:

1/2 × 10 × 7 = 35 m²

Regular Pentagon

Formula:

Area = 5s² / (4 × tan(π / 5))

A regular pentagon has five equal sides and five equal interior angles.

Here, s represents the side length.

If the side length is 2 m, the area is approximately:

6.88 m²

Regular Hexagon

Formula:

Area = 6s² / (4 × tan(π / 6))

A regular hexagon has six equal sides and six equal interior angles.

A familiar example is the hexagonal structure found in honeycomb.

If the side length is 2 m, the area is approximately:

10.39 m²

Regular Octagon

Formula:

Area = 8s² / (4 × tan(π / 8))

A regular octagon has eight equal sides.

One familiar real-world example is the shape of a standard stop sign.

If the side length is 1 m, the area is approximately:

4.83 m²

Annulus (Ring)

Formula:

Area = π × (outer radius² − inner radius²)

An annulus is the ring-shaped region between two concentric circles.

You can think of it as:

• A washer
• A circular pathway
• A ring-shaped garden bed
• A circular border around an open center

The calculation is straightforward: find the area of the larger circle and subtract the area of the smaller circle.

For example, if the outer radius is 3 m and the inner radius is 1 m:

π × (3² − 1²) ≈ 25.13 m²

The annulus therefore has an area of approximately 25.13 m².

The inner radius must be smaller than the outer radius.

Irregular Quadrilateral

Formula:

Area = 1/2 × diagonal × (height 1 + height 2)

For an irregular quadrilateral that meets the required geometric conditions, you can use a diagonal to divide the shape into two triangles and then add their areas together.

You need:

• One diagonal
• Two perpendicular heights measured relative to that diagonal

For example, if the diagonal is 10 m and the two heights are 3 m and 4 m:

1/2 × 10 × (3 + 4) = 35 m²

This method depends on having the correct diagonal and corresponding perpendicular heights. It should not be treated as a universal formula for every possible quadrilateral measurement setup.

Regular Polygon

Formula:

Area = n × s² / (4 × tan(π / n))

Where:

• n = number of sides
• s = length of each side

This formula applies to regular polygons, where all sides have the same length and all interior angles are equal.

The calculator supports regular polygons with 3 to 100 sides.

Regular pentagons, hexagons, and octagons are all special cases of this general formula.

For example, when n = 6 and the side length is 2 m, the area is approximately 10.39 m², matching the regular hexagon formula above.

Input Units and Output Units Can Be Different

One useful feature of an Area Calculator is that your measurement units and final area units do not have to be the same.

For example, suppose you measure a room in centimeters:

• Length = 350 cm
• Width = 420 cm

You can enter those measurements directly and choose square meters as the output unit.

The calculator handles the necessary conversion before displaying the final area.

This means you do not have to manually convert every measurement before doing the calculation.

Why Are Area Conversions Different From Length Conversions?

There is an important detail to remember: area units are squared, so area conversions do not use the same numerical factor as simple length conversions.

For example:

1 m = 100 cm

But:

1 m² = 10,000 cm²

That’s because:

1 m² = 1 m × 1 m

and:

100 cm × 100 cm = 10,000 cm²

So if a room measures 350 cm × 420 cm:

350 × 420 = 147,000 cm²

Converting that result gives:

147,000 cm² = 14.7 m²

Finding a Missing Dimension From a Known Area

An Area Calculator does not have to work only in one direction.

If you already know the target area, you can sometimes work backward to find an unknown dimension.

For example:

Known Area and Width → Find Length

Suppose a room needs to have 30 m² of floor area and its width is already fixed at 5 m.

Length = Area ÷ Width

30 ÷ 5 = 6 m

The required length is therefore 6 m.

Known Area → Find Circle Radius

Suppose you want a circular area of 50 m².

The radius can be found using:

radius = √(Area ÷ π)

So:

radius ≈ √(50 ÷ π) ≈ 3.99 m

This type of reverse calculation can be useful when planning room dimensions, circular spaces, garden areas, or other designs with a specific target area.

There is one natural requirement: at least one relevant dimension must remain unknown. If every relevant measurement is already fixed, there is no unknown value left to solve for.

What Does the Result Mean?

If the Area Calculator gives you a result of:

24 m²

it means that the shape covers a two-dimensional area equivalent to 24 squares, each measuring 1 m by 1 m.

That’s why area is expressed in square units.

For example:

meter × meter = square meter

The result can be useful for:

• Estimating flooring requirements
• Estimating the surface area of a wall
• Planning lawns and garden beds
• Comparing plots of land
• Planning tables, carpets, and other flat surfaces
• Estimating the area of circular spaces
• Calculating ring-shaped areas

However, geometric area is not necessarily the same as the amount of material you need to buy.

For example, flooring projects may involve cutting waste, fitting around corners, or packaging constraints. Painting projects may require you to account for windows, doors, multiple coats, and the coverage rate of the paint.

The calculator gives you the mathematical area. Real-world material requirements depend on the specific project.

What Rules and Data Does the Calculator Use?

The Area Calculator uses standard geometric area formulas based on the shape and measurements you provide.

There are a few basic requirements that need to be met for the calculation to make sense.

Dimensions Must Be Greater Than Zero

Lengths, widths, heights, radii, and side lengths used for physical area calculations must be valid numbers greater than zero.

Sector Angles Must Be Valid

A sector angle must be:

• Greater than 0°
• Less than or equal to 360°

An angle of 360° represents a complete circle.

Regular Polygons Need a Valid Number of Sides

The number of sides must be:

• An integer
• At least 3
• No more than 100

The Inner Radius Must Be Smaller Than the Outer Radius

For an annulus, the outer radius must be greater than the inner radius.

Required Measurements Must Be Provided

Each shape has its own required measurements.

For example, a rectangle needs a length and width, while a sector needs a radius and central angle.

If a required measurement is missing, there is not enough information to determine the area.

Can I Trust the Result?

When the correct shape and measurements are entered, the calculation is reliable because it is based on standard mathematical geometry formulas rather than a rough estimate.

There are still a few things that affect the final result.

Choose the correct shape.

If the real area is circular but you use a rectangle formula, the calculation will not represent the actual shape.

Measure accurately.

The calculator can process the numbers accurately, but it cannot correct an inaccurate measurement.

For example, if a room is actually 4.02 m wide but you enter 4 m, the calculator will correctly calculate the area for a width of 4 m. The difference comes from the measurement, not the formula.

Use the appropriate units.

Pay particular attention when working with centimeters, meters, feet, inches, or other units.

Provide the necessary information.

If a required dimension is missing, the area cannot be determined.

Calculations involving π can produce long decimal values, so the displayed result may be rounded to make it easier to read.

In other words, it is better to say that the mathematical calculation is highly precise rather than claim that every result is “100% accurate.” The quality of the final answer ultimately depends on the quality of the measurements you enter.

How the Area Calculator Helps

The value of an Area Calculator is not just that it saves you a few button presses.

It can help you:

• Automatically apply the appropriate formula for the selected shape
• Avoid having to memorize dozens of geometry formulas
• Reduce common manual calculation mistakes
• Calculate the area of 17 different geometric shapes
• Work with different length and area units
• Find a missing dimension when enough information is available
• Review the formula and calculation steps
• Learn and review geometry
• Check math calculations
• Estimate areas for home improvement
• Plan designs and spaces
• Estimate land and surface areas
• Handle everyday measurement problems

For a simple rectangle, you can easily calculate the area yourself.

But when you are dealing with a sector, annulus, ellipse, rhombus, or a regular polygon with many sides, having the appropriate formula ready can save a lot of time.

Which Shape Should I Choose?

Not sure which shape to use? Start with the basic geometry.

If the shape is a regular polygon, you can use the Regular Polygon option and enter the number of sides and side length.

Real-World Uses of Area Calculations

Area calculations are not limited to math classrooms. They are useful in many everyday situations.

Flooring

Measure the length and width of a rectangular room to determine the floor area.

Area = length × width

The calculated area gives you a starting point for estimating how much flooring is needed. Actual purchasing decisions should also account for cutting waste and other installation factors.

Painting

Wall area can help you determine how much surface needs to be covered.

In practice, you may also need to account for doors, windows, the number of coats, and the paint’s coverage rate.

Gardening

Area can help you plan lawns, flower beds, vegetable gardens, and planting areas.

Circular garden beds can be calculated using the circle formula, while ring-shaped beds can use the annulus formula.

Land and Property

Land and property are commonly described using area.

Depending on the location and measurement system, you may see units such as square meters, square kilometers, square feet, square yards, or acres.

Circular Tables

If you know the radius of a circular tabletop, you can calculate its area.

This can be useful when planning tablecloths, glass surfaces, decorative covers, or other materials.

Ring-Shaped Areas

Circular paths, garden borders, landscaped rings, and other ring-shaped spaces can be calculated using the annulus formula.

Area vs Perimeter vs Volume: A Quick Example

Consider a room that is 6 m long, 4 m wide, and 2.8 m high.

Perimeter

2 × (6 + 4) = 20 m

This measures the distance around the room and can be useful when estimating baseboard or other boundary materials.

Area

6 × 4 = 24 m²

This measures the floor surface and can be used when estimating flooring.

Volume

6 × 4 × 2.8 = 67.2 m³

This measures the three-dimensional space inside the room.

Knowing which measurement you actually need is the first step toward choosing the right calculator.

Final Thoughts

Calculating area is usually straightforward once you know the correct shape and formula. The challenge is that real-world shapes are not always simple rectangles.

A circle requires π. A triangle needs a base and perpendicular height. A sector requires an angle. A rhombus can be calculated from its diagonals. A regular polygon depends on both its side length and number of sides. And sometimes you already know the area and need to work backward to find a missing dimension.

That’s where an Area Calculator can save time.

Choose the shape, enter the measurements, select your units, and let the calculator handle the formula and calculation. Whether you’re checking a geometry problem, planning a room, estimating a garden, or simply trying to answer “How much space does this shape cover?”, the right area formula can turn a complicated-looking question into a straightforward calculation.